The flow rate increases 100-fold (one hundred-fold) Would be a more idiomatic way of saying this, however, the questioner asks specifically about the original phrasing. The above Ngram search would suggest that a one hundred has always been less frequently used in written language and as such should probably be avoided. Your other suggestion of by one hundred times is definitely better than a ...
People often say that percentages greater than 100 make no sense because you can't have more than all of something. This is simply silly and mathematically ignorant. A percentage is just a ratio between two numbers. There are many situations where it is perfectly reasonable for the numerator of a fraction to be greater than the denominator.
relating to 100 years : marking or beginning a century, with the example "the centurial years 1600 and 1700". But there is a word that is widely used to indicate the range of years or centuries covered by an article or book: history.
2 Use 100% when you are stating mathematical thought like statistics. Use "one hundred percent" when you are stating non-mathematical thought like a story.
In a scientific or mathematical context they might occur, in which case you should use standard index form 1×10¹⁰⁰ for one followed by 100 zeros. There is the joke word "googol" for this.
The first example is incorrect. The second and third examples are both correct. Which one you use is mostly a matter of preference, although a hundred appears more frequently than one hundred. There is also another form, an hundred, which was common in the past, but has mostly fallen out of use. See Google Ngram Viewer: a hundred, an hundred, one hundred:
If soap A kills 100% and soap B kills 99.99% of bacteria, the remaining amount of bacteria after applying A (0%) is infinitely smaller than the remaining amount of bacteria after applying B (0.01%). Therefore A is much, much better. You can see from these examples that 0.01% gap behaves differently across the percentage scale.
It leaves no room for ambiguity or mistake. Bottom line. If a student is given a mixed number or mixed fraction (same thing, slightly different name) such as 57 20/100 (fifty seven and twenty hundredths) then you say it as a fraction, using 'and', as I just wrote it in words.
37 Wikipedia lists large scale numbers here. As only the 10 x with x being a multiple of 3 get their own names, you read 100,000,000,000,000,000,000 as 100 * 10 18, so this is 100 quintillion in American and British English and 100 trillion in most (non-English speaking) other places.
